Solar System planetary tests of dot c-c - General Relativity and Quantum Cosmology

Abstract: Analytical and numerical calculations show that a putative temporal variationof the speed of light c, with the meaning of space-time structure constantc ST, assumed to be linear over timescales of about one century, would induce asecular precession of the longitude of the pericenter \varpi of a test particleorbiting a spherically symmetric body. By comparing such a predicted effect tothe corrections \Delta\dot\varpi to the usual Newtonian-Einsteinian perihelionprecessions of the inner planets of the Solar System, recently estimated byE.V. Pitjeva by fitting about one century of modern astronomical observationswith the standard dynamical force models of the EPM epehemerides, we obtained\dot c-c =0.5 +- 2\times 10^-7 yr^-1. Moreover, the possibility that \dotc-c eq 0 over the last century is ruled out at 3-12\sigma level by taking theratios of the perihelia for different pairs of planets. Our results areindependent of any measurement of the variations of other fundamental constantswhich may be explained by a variation of $c$ itself with the meaning ofelectromagnetic constant c EM. It will be important to repeat such tests ifand when other teams of astronomers will estimate their own corrections to thestandard Newtonian-Einsteinian planetary perihelion precessions.